a storage crate has the dimensions : 12ft * 6ft *5ft. how many cube-shaped boxes measuring 8 inches in length could be stacked completely within the cube??
To find out how many cube-shaped boxes measuring 8 inches can be stacked completely within the storage crate, we need to convert the dimensions of the crate to inches since the length of the cube is given in inches.
The dimensions of the crate are:
Length = 12 ft = 12 * 12 inches = 144 inches
Width = 6 ft = 6 * 12 inches = 72 inches
Height = 5 ft = 5 * 12 inches = 60 inches
Now, let's calculate the volume of the crate:
Volume of the crate = Length * Width * Height
Volume of the crate = 144 inches * 72 inches * 60 inches = 622,080 cubic inches
Next, we need to find the volume of a single cube-shaped box:
Volume of the cube-shaped box = Length^3
Volume of the cube-shaped box = 8 inches * 8 inches * 8 inches = 512 cubic inches
Finally, we can determine how many cube-shaped boxes can completely fit within the storage crate by dividing the volume of the crate by the volume of a single cube-shaped box:
Number of cube-shaped boxes = Volume of the crate / Volume of a single cube-shaped box
Number of cube-shaped boxes = 622,080 cubic inches / 512 cubic inches ≈ 1215
Therefore, approximately 1215 cube-shaped boxes measuring 8 inches in length can be stacked completely within the given storage crate.